The number of simple modules of the Hecke algebras of type G(r,1,n)

Author

Susumu Ariki and Andrew Mathas

Status

Research Report 98-14
Date: 8 July 1998

Abstract

This paper is concerned with the problem of classifying the simple modules
of a Hecke algebra H of type G(r,1,n). Using Kac-Moody algebra
techniques we first show that the number of simple H-modules is, in
a certain sense, independent of the choice of parameters for the Hecke algebra.
Next, by studying Kashiwara's crystal graph, we show that the simple
H-modules are indexed by the set of Kleshchev
multipartitions and we give a generating function for this set.

As an application of these results we give a classification of the number
of simple modules of an affine Hecke algebra of type A.